Flu Shot Dosage A hospital in a developing nation is forced to manually put the

Question

Flu Shot Dosage

A hospital in a developing nation is forced to manually put the flu shot vaccine into syringes. The recommended dosage for the flu shot is 0.5mL. The local health authorities define all syringes that have less than 0.45ml or more than 0.55mL as defective. In a sample of 100 syringes, the hospital’s quality control officer finds the average dosage to be 0.5mL. The standard deviation of the dosage is 0.02 mL and the distribution of the dosages resembles a normal distribution reasonably closely.

1) What percentage of the manually filled syringes will be outside the specification limits provided by the local health authorities? (Please answer in decimal form.)

2) To what level would the hospital have to reduce the standard deviation of the operation if his goal were to obtain a capability score of Cp=4/3 (i.e., get 63 defects per million)?

Explanation / Answer

Flu Shot Dosage normal distribution mean, m 0.5 mL UCL 0.55 mL LCL 0.45 mL std dev, s 0.02 mL sample size, n 100 syringes 1) What percentage of the manually filled syringes will be outside the specification limits provided by the local health authorities? UCL = m + z* s LCL = m - z* s where, z gives us the percentage within the specification limits. solving for z from: 0.55= 0.5 + 0.02*z or 0.45 = 0.5 - 0.02*z z 2.5 the corresponding probability for 2.5 value of z is 0.99379 hence, 0.99 i.e. 99% syringes are within the specification limits Hence, The percentage of the manually filled syringes will be outside the specification limits provided by the local health authorities is 0.00621 2) To what level would the hospital have to reduce the standard deviation of the operation if his goal were to obtain a capability score of Cp=4/3 (i.e., get 63 defects per million)? Cp = (UCL - LCL)/6s Current Cp 0.83 required Cp 1.3 1.3 = (0.55-0.45) / 6*s Calculate for s: s = 0.013 the hospital have to reduce the standard deviation of the operation to 0.013 from 0.02, if the goal were to obtain a capability score of Cp=4/3

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